Rules for Time Travelers

With the new Star Trek out, it’s long past time (as it were) that we laid out the rules for would-be fictional time-travelers. (Spoiler: Spock travels to the past and gets a sex change and becomes Kirk’s grandfather lover.*) Not that we expect these rules to be obeyed; the dramatic demands of a work of fiction will always trump the desire to get things scientifically accurate, and Star Trek all by itself has foisted half a dozen mutually-inconsistent theories of time travel on us. But time travel isn’t magic; it may or may not be allowed by the laws of physics — we don’t know them well enough to be sure — but we do know enough to say that if time travel were possible, certain rules would have to be obeyed. And sometimes it’s more interesting to play by the rules. So if you wanted to create a fictional world involving travel through time, here are 10+1 rules by which you should try to play.

0. There are no paradoxes.

This is the overarching rule, to which all other rules are subservient. It’s not a statement about physics; it’s simply a statement about logic. In the actual world, true paradoxes — events requiring decidable propositions to be simultaneously true and false — do not occur. Anything that looks like it would be a paradox if it happened indicates either that it won’t happen, or our understanding of the laws of nature is incomplete. Whatever laws of nature the builder of fictional worlds decides to abide by, they must not allow for true paradoxes.

1. Traveling into the future is easy.

We travel into the future all the time, at a fixed rate: one second per second. Stick around, you’ll be in the future soon enough. You can even get there faster than usual, by decreasing the amount of time you experience elapsing with respect to the rest of the world — either by low-tech ways like freezing yourself, or by taking advantage of the laws of special relativity and zipping around near the speed of light. (Remember we’re talking about what is possible according to the laws of physics here, not what is plausible or technologically feasible.) It’s coming back that’s hard.

2. Traveling into the past is hard — but maybe not impossible.

If Isaac Newton’s absolute space and time had been the correct picture of nature, we could simply say that traveling backwards in time was impossible, and that would be the end of it. But in Einstein’s curved-spacetime universe, things are more flexible. From your own personal, subjective point of view, you always more forward in time — more technically, you move on a timelike curve through spacetime. But the large-scale curvature of spacetime caused by gravity could, conceivably, cause timelike curves to loop back on themselves — that is to say, become closed timelike curves — such that anyone traveling on such a path would meet themselves in the past. That’s what respectable, Einstein-approved time travel would really be like. Of course, there’s still the little difficulty of warping spacetime so severely that you actually create closed timelike curves; nobody knows a foolproof way of doing that, or even whether it’s possible, although ideas involving wormholes and cosmic strings and spinning universes have been bandied about.

3. Traveling through time is like traveling through space.

I’m only going to say this once: there would be no flashing lights. At least, there would only be flashing lights if you brought along some strobes, and decided to start them flashing as you traveled along your closed timelike curve. Likewise, there is no disappearance in a puff of smoke and re-appearing at some other time. Traveling through time is just like traveling through space: you move along a certain path, which (we are presuming) the universe has helpfully arranged so that your travels bring you to an earlier moment in time. But a time machine wouldn’t look like a booth with spinning wheels that dematerializes now and rematerializes some other time; it would look like a rocket ship. Or possibly a DeLorean, in the unlikely event that your closed timelike curve started right here on Earth and never left the road.

Think of it this way: imagine there were a race of super-intelligent trees, who could communicate with each other using abstract concepts but didn’t have the ability to walk. They might fantasize about moving through space, and in their fantasies “space travel” would resemble teleportation, with the adventurous tree disappearing in a puff of smoke and reappearing across the forest. But we know better; real travel from one point to another through space is a continuous process. Time travel would be like that.

4. Things that travel together, age together.

If you travel through time, and you bring along with you some clocks or other objects, all those things experience time in exactly the same way that you do. In particular, both you and the clocks march resolutely forward in time, from your own perspective. You don’t see clocks spinning wildly backwards, nor do you yourself “age” backwards, and you certainly don’t end up wearing the clothes you favored back in high school. Your personal experience of time is governed by clocks in your brain and body — the predictable beating of rhythmic pulses of chemical and biological processes. Whatever flow of time is being experienced by those processes — and thus by your conscious perception — is also being experienced by whatever accompanies you on your journey.

5. Black holes are not time machines.

Sadly, if you fell into a black hole, it would not spit you out at some other time. It wouldn’t spit you out at all — it would gobble you up and grow slightly more corpulent in the process. If the black hole were big enough, you might not even notice when you crossed the point of no return defined by the event horizon. But once you got close to the center of the hole, tidal forces would tug at you — gently at first, but eventually tearing you apart. The technical term is spaghettification. Not a recommended strategy for would-be time adventurers.

Wormholes — tunnels through spacetime, which in principle can connect widely-separated events — are a more promising alternative. Wormholes are to black holes as elevators are to deep wells filled with snakes and poisoned spikes. The problem is, unlike black holes, we don’t know whether wormholes exist, or even whether they can exist, or how to make them, or how to preserve them once they are made. Wormholes want to collapse and disappear, and keeping them open requires a form of negative energies. Nobody knows how to make negative energies, although they occasionally slap the name “exotic matter” on the concept and pretend it might exist.

6. If something happened, it happened.

What people want to do with time machines is to go into the past and change it. You can’t. The past already happened, and it can’t un-happen. You might wonder what’s to stop you from jumping in your time machine, finding your high-school self, and convincing them that they really shouldn’t go to the senior prom after all, thereby saving yourself all sorts of humiliation. But if you really did go to the prom, then that can’t happen. The simple way out, of course, is to suppose that travel into the past is simply impossible. But even if it’s not, you can’t change what already happened; every event in spacetime is characterized by certain things occurring, and those things are fixed once and for all once they happen. If you did manage to go back in time to your years in high school, something would prevent you from dissuading your younger self from doing anything other than what they actually did. Even if you tried really hard.

7. There is no meta-time.

The least realistic time-travel movie of all time might be Back to the Future. When Marty McFly changes the past (violating Rule 6), the future “instantaneously” changes. What the hell is that supposed to mean? Time measures the temporal interval between different events in spacetime, and can be quantified by clocks. There is no set of clocks outside the universe, with respect to which you can go muck around in the past and have effects propagate into the future “at the same time.” Likewise, your brain is not going to change to remember things differently, nor will any other record-keeping device such as diaries or photographs or embarrassing sex tapes. Sorry about that.

8. You can’t travel back to before the time machine was built.

Right now, at the particular place you are sitting, at the time when you are sitting there, one of two things is true: either there is a closed timelike curve passing through that point in spacetime, or there is not. And that situation will never change — no matter what clever engineers may do in the future, if they create closed timelike curves they cannot pass through events in spacetime through which closed timelike curves did not pass (corollary of Rule 6). Or in plain English: if you build a time machine where there wasn’t one before, it may be possible for future travelers to come back to that time, but nothing can help you go back to times before the machine was built.

9. Unless you go to a parallel universe.

Parallel universes — the kind we contemplate in the many-worlds interpretation of quantum mechanics (MWI) — provide potential loopholes for some of the above rules. According to the MWI, there exist different “branches” of the wave function of the universe, distinguished by different observed outcomes for the measurement of quantum events. In the celebrated Schrödinger’s cat thought experiment, there is a “universe” where the cat is alive, and one where it is dead. Some imaginative (but respectable) physicists, especially David Deutsch, have speculated that we could combine this idea with the possibility of closed timelike curves to contemplate travel into the past of a different universe. If time travel is unlikely, this idea is (unlikely)2, but it’s not inherently paradoxical.

If you could travel to the past in a different branch of the wave function, then we are allowed to contemplate changing that past in a self-consistent way, because it’s no longer really “your” past. So almost all cinematic invocations of time travel — where they are constantly mucking about, changing the past in crucial ways — would have to appeal to something along these lines to make any sense. But even if you can change what you thought was the past, all of the rules of continuity and sensibility still apply — no flashing lights, no disappearing, no sudden changes in the future, no re-writing of your memories, etc.

10. And even then, your old universe is still there.

Remember Rule 0: no paradoxes. If you have reliable records of having made some unwise decisions regarding your social life in high school, then those decisions were made, and can’t be un-made. Even if you go into a different branch of the wave function, where you bestow some wisdom-of-experience on your younger self, you would only be changing the history of that universe. There is still the universe you left behind, with all of your bad decisions still intact. That’s life in the multiverse for you. It remains for future scholars to write Ph.D. theses along the lines of Utility Functions and Moral Dilemmas in an Ensemble of Multiple Interacting Universes. But it’s just a matter of time.

[* Update: Spock does not actually travel backwards in time and become Kirk’s grandfather, nor lover, nor does he write Shakespeare’s plays. That was a “joke.” I am reliably informed that the Spoiler Patrol and Internet Rectitude Society does not appreciate “jokes.”]

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229 Responses to Rules for Time Travelers

  1. Sean says:

    I should have said “grandmother.” On the internet, take nothing for granted.

  2. A footnote on Nahin: Anyone who has taught a course on the history of radio and has a cat
    named Heaviside has to be a great writer. The book is very readable. Nahin has a good
    command both of physics and of the science-fiction literature, and the book is about both.
    More technical stuff is relegated to very large appendices.

    I’ll sign off with a quote from Kip Thorne:

    “CALIFORNIA magazine, in an article on “The Man Who Invented Time Travel”, even ran a photograph of me doing physics in the nude on Palomar Mountain. I was mortified—not by the photo, but by the totally outrageous claims that I had invented time machines and time travel.”

    I now see that Amara (who came to my wedding back in 2002) has already quoted it
    in this very blog:

  3. Bee says:

    Sean, a question to you that I’ve recently been scratching my head over. It’s not really about time travel but about superluminal signaling, but we know both are related to each other. If you leave aside problems with defining a QFT, superluminal propagation isn’t a priori a problem as long as curves are, as you point out, consistent. Now that’s all well and fine, and one can show that tachyons aren’t necessarily problematic (and I believe there was a SciAm article recently with Albert that made a similar statement in relation to collapse of the wavefunction).

    But I am not sure this can work once you take into account the arrow of time. Thus, since you are the expert on the issue, what do you think? I was thinking roughly the following: take a lightbulb. It will emit photons outwards on the lightcone. Now let it emit some sort of superluminal particles. They will move outwards on a wider cone. Thermodynamics would tell you you are likely to observe these shells of light to increase in radius and decrease in amplitude but it’s extremely unlikely to find some set of photons moving inwards and collecting to a point. At least I’ve never seen that. The problem is then of course that there are Lorentz transformations that would topple part of the the superluminal lightcone upside down, depending on the direction of the boost, such that these particles would indeed collect to a point rather than expand. That would certainly look odd, but it isn’t really clear to me whether it’s problematic?



  4. tacitus says:

    I would settle for just being able to observe the past.

    Of course, given that the past includes what happened seconds ago, there would be horrendous privacy issues, but the chance to observe historical events as they really happened would have profound ramifications for the present and future.

    Religious adherents of all faiths would rightly be very nervous about what we would find about their origins. Criminals would find it almost impossible to get away with any crime. All forensic disciplines would be revolutionized–archaeology, history, paleontology, etc.–and evolution could be studied first hand. Reality TV would become the standard as producers rush to edit all the great moments in history down to hour-long segments, not to mention what it would do for the porn industry…

  5. Sean says:

    B, I think that it is very problematic, if I understand what you mean. One way of saying it is: if there are closed timelike curves, the entropy can’t increase monotonically along them. I.e. a consistent arrow of time can’t be defined. And I think there would be a similar problem for tachyons, basically as you point out, although it’s not as straightforward.

    Which is why I tend to think that superluminal propagation and CTC’s are very problematic in the real world. Even if you can consistently define propagation in their presence, it’s extremely restricted, in ways we would ordinarily consider to be wildly anti-thermodynamic. It’s exactly like having a low-entropy future boundary condition, because your future is now effectively tied to your past. And future boundary conditions are something we can contemplate, but they lead to funny acausal behavior. Not logically impossible, but incompatible with conventional causality. (See chapter six of the book!)

  6. Low Math, Meekly Interacting says:

    “No Paradoxes” seems to imply weird things. It’s almost as if my intention to go back in time and commit some paradoxical action would bring some calamity upon me to prevent it, whereas if I set forth pure of heart and adhering scrupulously to the Temporal Prime Directive, all would be well.

  7. gandeep says:

    Hi Sean

    I had a question similar to Bee’s question above. As you said traveling in time must be a continuous process. So in order to get to a past instant one will have to travel back through time. As you once explained earlier (when you wrote about ‘The curious case of Benjamin Button’) it is not possible to have incompatible arrows of time. So for the person ‘going back in time’ all biological processes like aging, remembering must still occur in the same ‘direction’ as the rest of the universe. So if we ‘go back in time’ it should not feel like going back in time all as still only the past would be remembered by us. Also we should get younger as we go more into the past. Is this reasoning correct?

    A broader question: Even if it is possible for a single particle to travel in a CTC in a certain spacetime, are new problems introduced by Thermodynamic considerations if a macroscopic object has to travel in a CTC?

  8. greg says:

    @Low Math – when dealing with non-MWI time travel, you run into questions about free will and determinism more than problems with paradoxes. if at some point in the future, you travel into the past, it’s because at that point on the time line leading up to the time you left, you appeared, whether you knew about it or not. Your appearing in the past already happened. You can’t not appear at the point in time!

    For those of you who enjoy time travel science fiction, if you haven’t already you should go read Robert Heinlein’s “All You Zombies”. It’s one of the best consistent time line stories out there.

  9. Low Math, Meekly Interacting says:

    @greg: Well, sure, but it’s still weird. So OK, you’ve got your block universe, and free will is an illusion. That doesn’t stop its inhabitants from thinking they’re making a choice when they set forth to screw with causality, or whatever, only to be somehow thwarted, as they simply must be, to avoid paradox. The rule is, then, that anyone who thinks they can influence the past such that it creates a paradox is wrong, always, but what’s not obvious (to me, anyway) is how nature goes about insuring this is always true.

    Many worlds gives me hives.

  10. Sean says:

    gandeep — The arrow of time can be defined locally; it’s okay (in principle) to have an arrow that points one way in one part of the universe, but differently from where it points in some very far-away part of the universe. The problem arises when two regions with purportedly different arrows are interacting with each other; that is very hard to sustain (probably impossible).

    So: if there were a closed timelike curve, we would age along it, and feel older when we finished our journey than when we started it, just as for any other journey. But we arrive at a part of the universe that was “earlier” in some approximate global time coordinate. The problem arises, again, if things moving along the closed timelike curve start interacting with the rest of the universe.

    There is a different but related problem for a macroscopic object that describes a closed loop all by itself. That is very difficult to imagine, since the state of the object at the “end” of its journey would have to be precisely the same as the state at the “beginning,” which for macroscopic objects is hard to pull off.

  11. rob says:

    Of course the real world doesn’t do analytic extensions, because the real world doesn’t have coordinates. But the real world does, at some level, solve the Einstein equations. So all that matters to me is whether it’s a solution or not. Obviously Kerr is an unrealistic model of the real world, at the very least because the real world isn’t stationary. But at a mathematical level we have very little handle on the fully nonlinear dynamics of GR, especially when there are Cauchy horizons involved.

    Now, I will admit, and I’m sure you know much more about the details of this than I do, that there are strong observational astrophysical and cosmological reasons to doubt the physical existence of white holes, even on top of their inherent instability. So this could moot any talk about exiting a black hole into the same universe. And I’ll also admit, as you pointed out, that even if a physical black hole were tied to a white hole in the past in the same universe, the United Federation of Planets would not have the power to bring that white hole into the vicinity (in whatever sense the word is meaningful) of its partner. So it’s obviously not a practical method of time travel, especially when you can just use warp drive to follow a spacelike path into your immediate causal past. I guess my main point is that compared to other time travel scenarios Star Trek has used in the past (like flying around the sun at a really high speed, for example), this one is a hell of a lot better.

    But at any rate, we’re way off on a tangent space, so I’ll drop it.

  12. Who made you God, and allowed you to decide the laws of time travel? Are you writing with the authority of logic or experience? My guess is logic, which is only as true as its premises. In the past there were things we didn’t know about space-time. My guess is there are still things we don’t know about space-time, and as our understanding of the universe changes/improves, our ability to move about in that universe will also change/improve. If we do live in a 4-(or 20)dimensional space time universe, and we can only move forward in time under normal circumstances, the solution to going to other parts of that space-time continuum is to get out of the space-time continuum completely and then reland in it wherever and whenever we want to. Your arguments about time travel suppose that there is an objective and unchanging reality. However, we each experience a subjective reality, and if, in my subjective reality I somehow manage to travel to far future or far past, then who is to say that did not happen to me? Again, I maintain, that your laws of time travel are only true if your premises are true, and that hasn’t been proven.

  13. TimG says:

    Like wds, above, I’m wondering how things look to the non-time-traveling observer.

    I get that for the time traveler inside the rocket ship time always appears to move forwards (unless she looks outside the window). But for the “stationary” observer watching from outside the rocket ship, wouldn’t there be some point where the rocket “doubled back” in time? That is, if he were to plot the rocket’s motion on time and space axes corresponding to his “stationary” reference frame, then there has to be some point where the time coordinate of the rocket had its maximum value. (That’s what we mean by traveling backwards in time, right? At some point your motion in spacetime takes you towards the past of the observer outside the rocket, rather than towards his future.)

    How would things look to the observer at that point? I’m imagining something like a particle anti-particle annihilation, in which one backwards-flying rocket ship collides and annihilates with the forward-flying rocket ship. But with macroscopic objects, this seems a bit bizarre, since from the non-time-traveling observer’s perspective both rockets would be partially overlapping with each other at the moment before the collision.

  14. dmduncan says:

    Regarding rule 9: We can’t travel to the “past” of an alternate universe either. What you might be trying to say is we might be able to travel to the present of an alternate universe which resembles the past of this universe, assuming that such alternate universes exist at all and if they do that they parallel the development of our own but are not parallel in time, so that a lateral shift from this one to the other brings us into a similar universe at an earlier stage of development. But that’s not time travel. It’s weird, but not time travel.

  15. Gabe says:

    So is #8 how one would get around a time-travel version of the Fermi Paradox?

  16. rickb says:

    One of the best time travel movies has to be “Primer”. While the rules of time travel in the movie appear to make it possible to change the past–which means parallel universes, I much prefer the single universe, can’t change anything time travel story– it gets the actual mechanics of moving back in time dead on.

  17. Hugo says:

    Not a problem really. The arrow of time, as the second law of thermodynamics are just statistical. Nothing Prohibits you of arranging light rays that would eventually converge to a metal filament and generate electrons. It’s highly improbable. though, unless you have a small number of electrons or a very small temperature. If something prevents the existence of tachyons I bet it would be causality, not thermodynamics.

  18. rickb says:

    In Feynman-Wheeler absorber theory, both advanced and retarded waves are emitted symmetrically both backwards and forwards in time, as long you have the appropriate boundary conditions correctly, i.e. you have perfect future absorber, all the advance waves get canceled out so you get an arrow of time with only retarded waves. Also John Cramer’s transactional interpretation of quantum mechanics uses this trick to explain non-locality in QM, it’s not superluminal, the “transaction” happens at the speed of light, it’s just that its backwards in time.

  19. Mark says:


    You might qualify your discussion by saying that you mean *intentional* time travel. After all, (spontaneous) time travel occurs all the time in relativistic quantum mechanics.

    The argument is trivial. Heuristically, the uncertainty principle implies that a particle can occasionally (but always uncontrollably) have greater speed than c. Equivalently, you can just compute the amplitude for a particle to be found outside its light cone, and you find that the answer is exponentially small but nonzero. A particle can jump backward in time, in which case it looks like its antiparticle.

    The whole reason why quantum mechanics and relativity are so conflicting (and why imposing both simultaneously is so constraining on the allowed physics) is precisely because of this light-cone leakage. Leakage of particles outside their forward light cones (which looks like backwards-time-traveling to certain Lorentz observers) explains why antiparticles are necessary (see, for example, Weinberg’s old GR book), as well as why particle creation/annihilation, particle indistinguishability, and the spin-statistics theorem are inevitable. (Though some of those are harder to prove.)

    So what you’re describing is the question of *controllable*, *deliberate* time travel. But it would be interesting to examine the spontaneous time travel of relativistic quantum mechanics in light of your list of 10+1 principles of time travel!

  20. What a cogent, succinct, well written piece. As a member of the “educated public” I thought I would respond to your post since, although most of the time your posts are written so we can understand, it seems like the responses all come from other scientists. I look forward to your book.

  21. Fernando says:

    I’m ignorant on the physics of space and time and, well, of physics in general, so maybe what I’m going to say is completely wrong because of something I have no idea. But for me, time travel makes no sense.

    For starters, does the past really exist? Is every moment in time a frozen moment, a “place” that can be visited? How would that be? I mean, how is that the specific position of every particle on the universe at a set time is somehow recorded and stored for eternity?

    Second, does time really exist? When I think about it, the only thing that seem to exist is motion. Just particles moving, and we call time our perception of this sequence of movements. Why would there be something like time travel if time is a human concept?

    Third, wouldn’t time travelling mean creating matter and energy? And isn’t that impossible? When you travel through time you bring atoms to a time where those atoms simply weren’t part of that universe. Say, if I travel from the year 2000 to 1999, I will have created entirely new matter on the year 1999, duplicated matter actually. That matter would only cease to be duplicated at the date of my time travel, when the me from before the time travel went away to 1999. And in away, it is almost like a teletransportation, because the matter that composed me from 2000 would simply disappear and reappear at where the time-traveler me is at on the exact moment of the time travel.

    And finally, isn’t any time travel paradoxical on it’s own? If I travel to the past, the reasons that made me want to travel are due to what has already happened, considering we live in a deterministic universe. My actions in the past affect the universe and set in motion the sequence of events that have created the me from the future which decided to travel back in time. So what caused me to travel through time had already happened, which was my time travel in the first place. It is retro-causality, can such thing even exist?

    Long post with confusing ideas that not even I’m sure it makes sense, probably won’t even be read.

  22. Guy says:

    I know one thing for sure, Every time we state absolutes, someone comes along and shatters that statement and proves otherwise. The only true statement would be that Mankinds dreams and imagination open doors that no one ever thought possible in the past. The Future holds Infinite inventions and discoveries. No one can say for sure today what is and what is not possible to do in the future. Endless inventors have proven that over and over.

    All of creation is none other than an endless amount of extremely complicated data and all we ever do while we are here is find ways to manipulate it and cause a ripple in the fabric of space time. remember ALL things are possible. The trick is discovering how to do it.


  23. Fernando says:

    Also, the idea that it is impossible to create the grandfather paradox, at the same time it makes sense, is so incredibly unlikely. I mean, if I try a terrorist nuclear attack on the past manhattan, the attack will fail because there was never a nuclear explosion on manhattan. So it means that no matter how many times I try to send a nuke back to the past, when the device gets there it will inevitably fail. Every single time. Let’s suppose those are bombs that have been tested and proved to work, somehow the bombs I pick to send back will always fail, even if they are produced the exact same way as the functional ones.

    And the grandfather paradox also makes it impossible for me to send back in time some gigantic object that would collide against earth. The grandfather paradox restricts time travel of objects of a specific mass to a specific position at a specific time.

  24. Low Math, Meekly Interacting says:

    If you’re boring, you could simply go with the “time travel* is impossible” option. Mother nature wouldn’t fault you.

    *of the deliberate, backwards, sci-fi variety, just to be clear

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